In this exponential growth function, after 5 hours it contains 1944mg and after 6 hours it contains 5832mg.
What is exponential function?
An exponential function is defined by the formula f(x) = aˣ, where the x is any real number , acts as an exponent. The exponential curve depends on the exponential function which depends on the value of the x.
Where a>0 and a is not equal to 1.
If many functions, “x” is a variable and “a” is a constant, which is the base of the function.
Given that, every hour, the mass of bacteria in a sample multiplies by 3.
Then the exponential function can be taken as f(x)= 3ⁿ x where f(x)= mass of bacteria, n=time(hours), x= original mass.
Here x= 8 mg
a) if n=5 hours then the exponential function will be
f(x)= 3⁵ × x
putting x=8 we get,
f(8)= 3⁵ × 8
= 1944
b) if n=6 hours then the exponential function will be
f(x)= 3⁶ × x
putting x=8 we get,
f(8)= 3⁶ × 8
= 5832
Hence, after 5 hours it contains 1944mg and after 6 hours it contains 5832mg.
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Write an equation of a line passing through (2, 2) and perpendicular to
У =
5* - 3.
The equation of a line passing through (2, 2) and perpendicular to y = 5x - 3 is y = -3x + 8.
What is equation?An equation is a mathematical statement between two expressions, with an equal sign (=) to indicate that both expressions are of the same value. Equations can be used to solve a variety of problems in mathematics, physics, chemistry, and other sciences. Additionally, equations are used to express relationships between different variables or unknowns.
The equation of a line passing through (2, 2) and perpendicular to the given line is y = -3x + 8.
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Triangle ABC is graphed on a coordinate grid. A is located at (8,4), B is located at (4,10), and C is located at (-2,4). The triangle is dilated with scale factor of 1/2 with the orgin as the center of dilation. Where would B’ be located at?
Answer:
A dilation is a transformation that changes the size of a figure while keeping its shape the same. In a dilation with a scale factor of 1/2 and the origin as the center of dilation, each point in the figure is moved away from the origin by a factor of 1/2.
To find the new location of point B, we can apply this dilation to the coordinates of point B. Point B is located at (4,10), so we can multiply each coordinate by 1/2 to find the new location.
B'(x',y') = (1/2)(x,y) = (1/2)(4,10) = (2,5)
So the new location of point B, B' is located at (2,5) in the coordinate plane.
Find the ratio of circles to squares in the diagram below.
OD
O
OOOO
O
Unsimplified ratio of circles to squares:
Just count them a
The ratio of any pair of corresponding sides is the RATIO OF SIMILARITY between any two similar figures. Simply put, when two figures are found to be similar, all of their associated side pairs have the same ratio.
What is a number's ratio?An ordered pair of numbers a and b, represented as a / b, is a ratio if b is not equal to 0. A proportion is an equation that sets two ratios at the same value. For instance, you could express the ratio as follows: 1: 3 if there is 1 boy and 3 girls (for every one boy there are 3 girls)
Since,
the number of circle in the given figure is 4
the number of squares in the given figure is 16
total number of figures is 20
Ratio is 4/20=1/5
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Match the solution to its expression.
Answer: Numbers 3, and 1
Step-by-step explanation:
1. (3/7)/(1/2) = 3/7 * 2 = 6/7 = Number 3
2. 3/4 * 1/4 = 3/4*4 = 3/16 = Number 1
Avelina and half as much as Gus if Gus are in 125 how much did Avelina earn
By solving a simple equation, we will see that Avelina earns $62.50
How much did Avelina earn?Here we know that Avelina earns half as much as Gus, then if we define the variables:
A = amount that Avelina earns.
G = amount that Gus earns.
Then we can write the equation:
A = G/2
That says that Avelina earns half as much as Gus.
We know that Gus earns $125. then we can replace that in the equation above:
A = $125/2
A = $62.50
Avelina earns 62.50 dollars.
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The equation below models the amount of profit the movie "Mission Impossible III" earned (in millions of dollars) at the Box Office each week "" since it's initial premiere.
Use this information to answer the questions attached.
Movie theater clipart 2 | Movie decor, Clip art, Movie theater
Question at position 5
5
2 points
Question at position 5
What does the "" mean in context of the problem?
Equations, their parts and how to solve them is discussed above.
What are algebraic expressions?In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.Mathematical symbols can designate numbers (constants), variables, operations, functions, brackets, punctuation, and grouping to help determine order of operations and other aspects of logical syntax.Given is an equation that models the amount of profit the movie (Mission Impossible III) earned (in millions of dollars) at the Box Office each week.
An equation is a mathematical statement that is made up of two expressions connected by an equal sign.
There are different parts of an equation which include coefficients, variables, operators, constants, terms, expressions, and an equal to sign.
The steps to solve a basic equation with one variable (linear) are given below:
Step 1 : Bring all the terms with variables on one side and all the constants on the other side of the equation by applying arithmetic operations on both sides. Step 2 : Combine all like terms (terms containing the same variablewith the same exponent) by adding/subtracting them.
Step 3 : Simplify it and get the answer.Therefore, equations, their parts and how to solve them is discussed above.
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suppose the three qubits held by alice, bob, and charlie are in a quantum state . if alice measures her qubit to be in the state , what is the probability that bob and charlie will find their qubits to be in the state ?
If Alice measures her qubit to be in the state, then the probability that Bob and Charlie will find their qubits to be in the state is 1/4. This is because the overall quantum state must collapse into the state Alice measured, so the probability of Bob and Charlie measuring the same state is 1/4.
In more detail, when Alice measures her qubit the three qubits must collapse into the state measured by Alice, due to the principles of quantum mechanics. This means that the probability of Bob and Charlie measuring the same state is 1/4, as the state measured by Alice is the only possible outcome. This is because the other three possible states (, and ) are no longer possible as they have been ‘erased’ by Alice’s measurement. To illustrate this, consider a quantum state of three qubits in the form of a ‘coin-flip’.
If Alice measures her qubit to be in the state, then the other two qubits must also be in the state. This is because the only possible outcomes of this quantum state are either all heads or all tails, and Alice’s measurement has ‘erased’ the other three possible outcomes (i.e. heads and tails, tails and heads, heads and heads). Therefore, the probability that Bob and Charlie will find their qubits to be in the state is 1/4.
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A 2-gallon container of laundry detergent costs $16.00. What is the price per cup?
The price of the laundry detergent per cup is $0.5.
Unit of measure of quantity.The measure of a quantity can be expressed by its unit. The unit can be converted from one to another if the quantity are related.
In this question, the gallon has to be expressed as cups. Thus the price of the laundry detergent can now be determined.
This implies that we can express gallon in terms of cups, we have;
1 gallon = 16 cups
So that,
2 gallons = 2*16
= 32 cups
Therefore;
the price of the laundry detergent per cup = $16/ 32
= $0.5
The price of the laundry detergent per cup is $0.5.
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What is the solution of log2?
The solution of log2 is approximately 0.30102999566. To solve for log2, one can use a calculator to calculate the logarithm of 2 to any given base.
To solve for log2, one can use a calculator to calculate the logarithm of 2 to any given base. For example, using a calculator set to base 10, one would enter the number 2 and then press the 'log' button. The answer would be 0.30102999566. This is the solution to log2. Alternatively, one could use a logarithm table to look up the answer. To do this, one would find the row labeled "base 10" and then find the column labeled "2". Then, find the corresponding number in the table, which would also be 0.30102999566.
The solution of log2 is approximately 0.30102999566.
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Long division
7/55
Pls help ASAP
Answer:55/7= 8
Step-by-step explanation:
It’s division
Answer:
7 with a remainder of 4
Step-by-step explanation:
Open the picture and look how i did.
Your Best Friend
s183960
Hope it helps! Don't Forget to rate!
How do you know if a quadratic function can be factored?
If the discriminant is a perfect square then it represents that quadratic function is factored.
As given in the question,
Standard quadratic function is expressed as :
ax² + bx + c = 0
Quadratic function can be factored by two methods :
1. Splitting of the middle term.
By splitting method it can be expressed as a product of linear function
A( x - u )( x -r )
2. By using quadratic formula : x = ( -b ± √b² -4ac ) /2a
Here discriminant = √b² -4ac
If the discriminant is a perfect square it is possible to factored quadratic equation.
Therefore, the value of discriminant is perfect square it represents that quadratic function is possible to factored.
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On opening night, Nutcracker on Ice sold out with 320 tickets sold. Adult tickets were $25 each and children tickets were $8 each. The total ticket sales was $6,130. How many adult tickets and how many children tickets were sold?
On opening night, the number of adult tickets and the number of children tickets were sold are respectively, 210 and 110
What are expressions?An expression is a sentence with at least two numbers or variables having mathematical operation. Math operations can be addition, subtraction, multiplication, division.
For example, 2x+3
Given that,
Total tickets sold = 320
Adult tickets = $25 each
Children tickets = $8 each
The total ticket sales= $6,130
Suppose, the number of adult tickets sold = x
So, the number of children tickets sold = 320 - x
Total sales = 6130
Total sales = adult tickets sold + children tickets sold
= 25×x + 8×(320 - x)
= 25x + 2560 - 8x
= 17x + 2560
6130-2560= 17x
x = 210
Now, number of children ticket = 320 - 210
= 110
Hence, The numbers are respectively, 210 and 110
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Which theorem is not a valid theorem to show that two triangles are congruent?
Methods that do not Prove Triangles to be Congruent.
1. AAA (angle angle angle)
AAA works fine to show that triangles are the similar shape (matching) but it does not apply to also show they are the same size, thus congruent!
Consider the following example at the right.
2. SSA (side side angle) or angle side side:
SSA is humorously called to as the “Donkey Theorem “.
This is not a universal method to solve triangles congruent because it cannot assurance that one unique triangle will be drawn!
The SSA (side side angle) mixture affords the possibility of creating zero, one, or two triangles.
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The equation of a line in slope intercept form is y=mx+b where m is the slope of the line.
Yes, that's correct. In the slope-intercept form, the equation of a line is given as y = mx + b where m is the slope of the line.
The variable "m" represents the slope of the line, which is a measure of how steep the line is. It is calculated as the ratio of the change in the y-coordinate to the change in the x-coordinate, also known as the rise over the run.
A line with a positive slope will rise as it moves to the right, while a line with a negative slope will fall as it moves to the right. A line with a slope of zero is a horizontal line and one with an infinite slope is a vertical line.
The variable "b" is the y-intercept, which is the point where the line crosses the y-axis. It is the value of y when x = 0.
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May I have some help please
Answer:
not increasing increasing
Step-by-step explanation:
I need help please!!
For f(4), it's 15. For determining x, it's 9.
For f(4), juet plug in 4 to x. 4(4) equals 16, minus 1 is 15.
For getting 35, we need to determine x. If you plug in 9 for f(x), 4(9) equals 36, minus 1 is 35.
Is the relationship linear, exponential, or neither?
No, the relationship is neither linear nor exponential.
What is an equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign.
Example:
2x + 4 = 8 is an equation.
We have,
Ordered pairs from the table.
(15, 10), (16, 20), (17, 40), and (18, 70)
Now,
The rate of change between two ordered pairs is not the same.
Rate of change between (15, 10) and (16, 20).
= (20 - 10)/(16 - 15)
= 10/1
= 10
Rate of change between (16, 20) and (17, 40).
= (40 - 20)/(17 - 16)
= 20/1
= 20
This shows that it is not a linear relationship.
We can not make it in an exponential form.
i.e y = [tex]a^x[/tex]
Thus,
The relationship from the table is not linear nor exponential.
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If U1 And U2 Are Orthogonal Unit Vectors Andv=Au1 + Bu2, Find v*u1
Honeybees beat their wings at very fast rates. In 9 seconds a honeybee can beat its wings 1917 times. In 23 seconds a honeybee can beat its wings 4899 times. Question Complete the table to show ratios that are equivalent to the ratio of time to number of wing beats for a honeybee. Enter a number in each box.
Answer: To complete the table, we need to find ratios that are equivalent to the ratio of time to number of wing beats for a honeybee.
We can start by finding the ratio of time to number of wing beats for the first data point:
9 seconds / 1917 wing beats = 9/1917
And the second data point:
23 seconds / 4899 wing beats = 23/4899
To find equivalent ratios, we can multiply or divide both parts of the ratio by the same number, without changing the value of the ratio. For example, we can divide both parts of the ratio by 9 to get:
9/1917 = (9/9) / (1917/9) = 1 / 213
We can also divide both parts of the ratio by 23 to get:
23/4899 = (23/23) / (4899/23) = 1/213
We can use this same method to find equivalent ratios for other values of time and number of wing beats.
Time (s) Number of wing beats Ratio
9 1917 9/1917 or 1/213
23 4899 23/4899 or 1/213
So, the ratio of time to a number of wing beats for a honeybee is equivalent to 1/213, regardless of the specific values of time and number of wing beats.
Step-by-step explanation:
Which is the cheapest per ounce: a 2 L bottle (67.6 oz.) of root beer at $1.49, a six-pack of 20-oz. bottles at $2.49, or a twelve-pack of 12-oz. cans at $2.99?
Root beer is the cheapest per ounce, i.e. root beer cost is 0.011 per ounce
What is the unit rate?When comparing two different kinds of numbers with distinct units, a rate is a ratio that is employed. The unit rate, on the other hand, shows how many units of one quantity are equal to one unit of another. When the rate's denominator is 1, we refer to the rate as a unit rate.
Given finding the cheapest per ounce,
A: a 2 L bottle (67.6 oz.) of root beer at $1.49
total weight of 2 liter bottle = 2 x 67.6 = 135.2 oz
135.2 oz = $1.49
1 oz = $1.49/135.2
1 oz = 0.011
root beer cost is 0.011 per ounce
B: a six-pack of 20-oz. bottles at $2.49,
total weight of 6 pack = 6 x 20 = 120 oz
120 oz = $2.49
1 oz = $2.49/120
1 oz = 0.21
bottles cost is 0.20 per ounce
C: a twelve-pack of 12-oz. cans at $2.99
total weight of 12 pack = 12 x 12 = 144 oz
144 oz = $2.99
1 oz = $2.99/144
1 oz = 0.021
can cost is 0.21 per ounce
Hence root beer is the cheapest per ounce.
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PLS DO NUMBER 10 WILL MARK BRAINLY AND ALSO GIVE AN ADDITIONAL 100 PTS IF CORRECT PLS HURRY. THANK YOU
Answer:
Step-by-step explanation:
the whole one or only one of them?
Answer:
i d k
Step-by-step explanation:
What is an equation of the line that passes through the point (8,-5) and is perpendicular to the line 5x+4y=24
Answer:
To find the equation of the line that passes through the point (8, -5) and is perpendicular to the line 5x + 4y = 24, you can use the following steps:
Find the slope of the line 5x + 4y = 24. To do this, you can rearrange the equation to the slope-intercept form y = mx + b, where m is the slope. So, you get y = -5/4 x + 6
Since the line is perpendicular to the line 5x + 4y = 24, the slope of the line is the negative reciprocal of the slope of the line 5x + 4y = 24 which is -4/5
Now, use the point-slope form of the equation of a line which is y - y1 = m(x - x1). So, the equation of the line that passes through the point (8, -5) and is perpendicular to the line 5x + 4y = 24 is :
y - (-5) = -4/5(x - 8)
y + 5 = -4/5x + 8/5
y = -4/5x + 13/5
So, the equation of the line is y = -4/5x + 13/5
I need help please hurry
Answer:
(-3,4) for the second problem
Step-by-step explanation:
This is a system of equations. We can solve the first for y and use that in the second.
Solve first one for y:
3x + y = -5
y = (-3x - 5)
Use this value for y in the second equation:
8x + 7(-3x - 5) = 4
8x - 21x -35 = 4
-13x = 39 (divide both sides by -13 here)
x = -3
Now put this value for x into one of the original equations to get y:
3(-3) + y = -5
-9 + y = -5
y = 4
You can put these x and y values into the original equations to check your work.
Determine whether each relation is a function. Find the domain and range.
Answer:
Step-by-step explanation: This is not a function because if you do a pencil check on the points two dots touch the pencil at the same time which does not make it a function.
four girls take turns flipping a fair coin until a head appears. what is the probability that the first girl is the first top lip a head
The probability that the first girl is the first to flip a head is 1/2.
The probability of appearing a head is 1/2.
If the number of toss required is odd as in one attempt represent odd number , we have following sequence of events
H, TTH, TTTTH.....
The required probability P will be
P = 1/2 + (1/2)³ + (1/2)⁵..........
As she flipped it in first go the probability will be 1/2.
The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true. An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty.
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HELP!!!! WILL MARK BRAINLYLIST 50 POINTS!
Jerry plans to begin saving money for a trip by putting $1 in a savings account the first month
and then adding enough to double the amount in the account each following month.
A. After he finishes contributing to the account, he will withdraw $500 to make a down
payment on the trip. Create a function to show how much money will be in the account if he
finishes contributing to the account after t months.
Type your response here:
b. Jerry plans to keep up this saving pattern until he can no longer afford it. At that time, he
hopes to have enough in his account for his trip. How much will be in the account, after
making the down payment, if the most he will be able to contribute in a month is $1,200?
Function that represents the amount of money in the account after t months under the provided condition is equal to A = [tex]2^{t - 1} -[/tex] 500.
What is meant by Function?Exactly one element of Y is assigned to each element of X in a mathematical function from a set X to a set Y. Both the set X and the set Y are referred to as the function's domain and codomain, respectively. The basic conception of functions was the relationship between fluctuating quantities and other variables.Exactly one element of Y is assigned to each element of X in a mathematical function from a set X to a set Y. Both the set X and the set Y are referred to as the function's domain and codomain, respectively. The basic conception of functions was the relationship between fluctuating quantities and other variables.Given,
Amount in the account
Frist month = $1
= [tex]2^{1-1}[/tex]
As per given condition,
second month = $2
= [tex]2^{2-1}[/tex]
Third month = $4
= [tex]2^{3-1}[/tex]
t = months.
Jerry withdraw $500 to make a down payment on the trip.
'A' represents the total amount left in the account
Required function as per given condition,
A = [tex]2^{t-1}[/tex] - 500
Hence, function representing the amount of money as per given condition in the account after t months is equals to A= [tex]2^{t-1}[/tex] - 500
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Simplify: –3(y 2)2 – 5 6y what is the simplified product in standard form?
The simplified product in standard form is -3y^4 - 30y.
What is algebraic equation ?
An algebraic equation is a mathematical statement that shows that two expressions are equal. The expressions can include numbers, variables, and mathematical operations such as addition, subtraction, multiplication, and division. For example, the equation 2x + 3 = 7 is an algebraic equation. In this equation, x is a variable, and the goal is to find the value of x that makes the equation true. Algebraic equations can be solved by using a variety of techniques, such as isolating the variable on one side of the equation, using inverse operations, or factoring. The solutions of an equation are the values of the variables that make the equation true.
To simplify the expression:
-3(y^2)^2 - 5*6y
First, we can simplify the inner parenthesis: (y^2)^2 = y^4
Next, we can simplify the constants: -3 * y^4 - 5 * 6y
Combining like terms: -3y^4 - 30y
So the simplified product in standard form is -3y^4 - 30y.
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The image of the point (0, 7)(0,7) under a translation is (-2, 5)(−2,5). Find the coordinates of the image of the point (5, -2)(5,−2) under the same translation.
The coordinates of the image of point (5, -2) under the same translation is (3, -4)
How to find the coordinates of the image of a point?Translation is a type of transformation that moves a figure or a function in a specific direction and distance without rotating or changing its size.
To solve the given, you can use the equation below:
image = point + translation
So we can say:
translation = image - point
translation = (-2, 5) - (0, 7)
translation = (-2-(0) , 5-7)
translation = (-2, -2)
Under the same translation, the coordinates of the image of the point (5, -2) will be:
image = point + translation
image = (5, -2) + (-2, -2)
image = (5+(-2) , -2+(-2))
image = (3, -4)
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Correct Question
The image of the point (0, 7) under a translation is (−2,5). Find the coordinates of the image of the point (5,−2) under the same translation.
What is the equation of this line? PLEASE HURRYYY!!!!!!
5/2 , 2.45, 2 2/5 , 6√ Put the numbers in order from least to greatest.
154b
Step-by-step explanation: